The fullscreen controller and cursor appear whenever the mouse moves. All it takes is bumping the table the mouse sits on, and the controller and cursor appear. This is REALLY irritating. It is especially bad since when the fullscreen controller is visible, the video rendering suddenly gets really slow for some reason, but that's another mystery.
The solution is simple: The fullscreen controller and cursor should only appear when the mouse moves to the bottom of the screen, and should only continue to appear while the mouse is within the controller, with the usual 1sec delay before they disappear. Then, moving the mouse anywhere away from the bottom of the screen will allow me to watch a movie without having to be really careful whenever I put the popcorn bowl back onto the table.